Math Problem Solver

\[ \frac{1}{10} + \frac{1}{15} = \frac{1}{6} = 0.1\overline{6} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{1}{10}\) and \(\frac{1}{15}\) is \(30\). \[ \begin{aligned} \frac{1}{10} + \frac{1}{15} &= \frac{1 \cdot 3}{10 \cdot 3} + \frac{1 \cdot 2}{15 \cdot 2} \\ &= \frac{3 + 2}{30} \\ &= \frac{5}{30} \\&= \frac{1}{6} \end{aligned} \]